Okay, you survived the draft with some decent guys.
RB--S. Alexander, Hearst, Barlow
WR--T. Holt, W. Jackson, Q. Ismail
TE--E. Johnson, D. Carswell
Your lineup suggests that you're probably in the nfl.com leagues. Wherever you are, look at your roster rules. You should be able to keep what you want for backups as long as you maintain a starting squad. This said, you can dump a kicker for sure. Probably a tight end too. Dilfer worries me this season, but if you want to hang onto him and see if things swing back his way, that's kewl.
Anyway, the reason to shed the excess baggage is so that you can grab some of that young blood that didn't get drafted. Guys like QB David Carr, RBs DeShaun Foster and T.J. Duckett, WR Deion Branch, etc. are probably all sitting in the free agent pool. Any of these guys is potentially worth more to you than a 2nd string kicker, injured player, or some veteran ranked 40th who has never put up decent points. Some of these guys may take a while to develop, some may go nowhere this season ... but if you get just one excellent player out of the bunch you could be looking pretty good by mid-season.
Fantasy football is practically a head to head match up between each of your starters and each of the opposing starters. The better each of your guys match up ... your #1 RB to their #1 RB, etc., the better your team will perform. Alexander, Holt, Johnson, Janikowski, and the Dolphins should all match up well against the opponents guys. You need to be concerned with your QB (Plummer isn't horrible; if it's ever gonna be "his year" this may be it), 1 RB, and 1 WR. Check out that free agent pool, look at backups who have become starters, and rookies who are all ready busting moves in pre-season, and add some depth at those crucial positions.
If you are going to keep Dilfer, I would pick up Hasselbeck (or whoever is declared the "backup") in a heartbeat.
Look at people's "sleeper picks", decide which ones you agree with, see if any of them are in the free agent pool. 14-man rosters leave alot of good talent floating around. You need to scoop some of it. Try to do this mainly through the leftover players. If you are inexperienced, trading can do you more harm than good. If you DO want to play with trading, YOU propose the trades. You might want to make someone a trade offer they "can't refuse", like 3 or 4 of the guys you're gonna dump anyways for 1 solid RB or WR. I think one good WR would put you above average. If you could then pull someone like Foster out've the free agent pool and have them perform well, you could be in contention. Good luck!